The valve train would NOT be my first suspect in your problem. I don't think they could leak enough oil to make it "spray tar". My 65 is a moderate oiler to the valve train at best. I don't think there is enough oil supply around the valve stems to make one spray tar. Of course if you are running choke full closed the engine would have a very high vacuum-- so maybe I'm wrong in that thinking ??
Matt asked good questions. I too would like to see the spark plugs.
You say it had water in the oil causing it to smoke white. When you had it apart, what did you find as the path for that mixture entering the cylinders ?
Oh, your carburetor needs a serious cleaning. My 65 takes very little choking at 20 degrees F.